1 Consider a normal distribution with a mean 70 and a stand

1. Consider a normal distribution with a mean = 7.0 and a standard deviation = 1.5. What proportion of the distribution is LESS THAN 5? 2.Consider a normal distribution with a mean = 7 and a standard deviation = 1.5. If 5,000 random data points are taken from this distribution, how many would you expect to be between 4.7 and 10.9? (Note - choose the best answer. It is possible your answer may differ by one or two due to rounding error.)

2. Consider a normal distribution with a mean = 7 and a standard deviation = 1.5. If 5,000 random data points are taken from this distribution, how many would you expect to be between 4.7 and 10.9? (Note - choose the best answer. It is possible your answer may differ by one or two due to rounding error.)

Solution

1) mean = 7

std dev = 1.5

to find p(x<5)

For x = 5, the z-value z = (5 - 7) / 1.5 = -1.33

Hence P(x < 5) = P(z < -1.33) = total area - [area to the left of -1.33] =1 - 0.0918 = 0.9082

= 90.82%